Interference

Beat note between two lasers

Two lasers that differ in colour by a tiny amount make a photodiode’s signal rise and fall at the difference of their frequencies. Light oscillates far too fast for any detector, but the difference can be slow enough to see on an oscilloscope.

What you are looking at

Both lasers meet at the cube and travel together to the photodiode. Its card shows an oscilloscope trace with the beat.

How the bench is set up

Two single-mode lasers at 632.8000 and 632.8001 nm, a 50:50 cube and a fast photodiode with 1 GHz bandwidth.

The theory

Two fields at frequencies $f_1$ and $f_2$ on one detector give a power

P(t) = P_1 + P_2 + 2\sqrt{P_1P_2}\,\cos\big(2\pi (f_1-f_2)\,t + \phi\big),

and a wavelength difference $\Delta\lambda$ gives a beat at $\Delta f = c\,\Delta\lambda/\lambda^2$ : 0.1 pm at 632.8 nm is about 75 MHz.

What to measure

Beat frequency c/λ₁ − c/λ₂

Read the beat frequency under the scope trace and compare with $c\Delta\lambda/\lambda^2$ .
Change the second laser’s wavelength and check the beat follows.

What the model leaves out

Real lasers drift by megahertz; here each line is narrow and fixed unless you give it a linewidth.

Things to try

Turn one laser’s polarisation to horizontal: the beat disappears, because crossed polarisations do not interfere.

References

B. E. A. Saleh and M. C. Teich (2019), Fundamentals of Photonics, 3rd edition, Wiley.

More experiments, and how the lab works, are in the laser lab’s overview.